The Space of Persistence Diagrams on n points Coarsely Embeds in Hilbert Space

Document Type

Presentation Abstract

Presentation Date

3-2-2020

Abstract

TDA (Topological Data Analysis) is a rapidly developing field that uses ideas from geometry and topology to get qualitative and quantitative information about the structure of data (finite sets of points in a metric space). One of the tools is the idea of Persistent Homology, which takes a one-parameter family of topological spaces and creates a signature called the persistence diagram that encodes useful information about the data set. For using existing kernel methods for analyzing such persistence diagrams, one needs to know how close the various metrics on the space on persistence diagrams can be to an inner product structure.

Using the methods of coarse geometry, we prove that the space of persistence diagrams on n points (with either the Bottleneck distance or a Wasserstein distance) coarsely embeds into Hilbert space. We also discuss various non-embeddability results when the number of points is not bounded.

This is joint work with Žiga Virk.

Additional Details

March 2, 2020 at 3:00 p.m. in Math 103
Refreshments at 4:00 p.m. in Math Lounge 109

This document is currently not available here.

Share

COinS